Izzy wrote a correct equality on the board: \(35 + 10 - 41 = 42 + 12 - 50\), and then subtracted 4 from both parts: \(35 + 10 - 45 = 42 + 12 - 54\). She noticed that on the left hand side of the equation all of the numbers are divisible by 5, and on the right hand side by 6. Then she took 5 outside of the brackets on the left hand side and 6 on the right hand side and got \(5(7 + 2 - 9)4 = 6(7 + 2 - 9)\). Having simplified both sides by a common multiplier, Izzy found that \(5 = 6\). Where did she go wrong?
A moth has made \(15\) little holes on a carpet of size \(4\text{m}\times 4\text{m}\). Is it possible to cut out a \(1\text{m}\times 1\text{m}\) square of the carpet that contains no holes? (The holes are assumed to be points)
The natural number \(a\) was increased by 1, and its square increased by 1001. What is \(a\)?
In a basket, there are 30 red and green apples. Among any 12 apples there is at least one red one, and among any 20 apples there is at least one green one. How many red apples and how many green apples are there in the basket?
The grandad is twice as strong as the grandma, the grandma is three times stronger than the granddaughter, the granddaughter is four times stronger than the dog, the dog is five times stronger than the cat and the cat is six times stronger than the mouse. The grandad, the grandma, the granddaughter, the dog and the cat together with the mouse can pull out the pumpkin from the ground, which they cannot do without the mouse. How many mice should be summoned so that they can pull out the pumpkin themselves?
If you have a piece of paper and some scissors, is it possible to cut a hole out of the paper that’s big enough for you to crawl through?
There are two hourglasses – one for 7 minutes and another for 11 minutes. An egg is boiled for 15 minutes. How can this time be measured with the help of the available hourglasses?
Two people had two square cakes. Each person made 2 straight cuts from edge to edge on their cake. After doing this, one person ended up with three pieces, and the other with four. How could this be?
How can you divide a pancake with three straight sections into 4, 5, 6, 7 parts?
Is it possible to bake a cake that can be divided by one straight cut into 4 pieces?